Rewrite as a simplified fraction. ${0.\overline{87} = {?}}$
Solution: Let $x$ equal the decimal. Set up two equations such that the digits after the decimal point are identical. ${\begin{align*}100x &= 87.8787...\\ 1x &= 0.8787...\end{align*}}$ Subtracting the two equations, we have: ${99x = 87}$ ${x = \dfrac{87}{99}} $ ${x = \dfrac{29}{33}} $